A nonlinear channelized model observer using Box-Cox transformation

Model observers (MOs) have been widely used for objective assessment of medical imaging systems. The performance of an MO on a specific task (e.g., tumor detection) provides a quantitative, task-based measure of image quality. For binary classification tasks, the Bayesian Ideal Observer (BIO) sets an upper performance limit and has been advocated for use in the objective assessment of imaging systems. However, except in very special cases, the BIO test statistic is a nonlinear function of the imaging data and cannot be determined analytically. The Hotelling observer (HO), which employs the optimal linear discriminant function, is often used as a surrogate for the BIO. When imaging data are Gaussian distributed with the same covariance matrices under the two hypotheses, the HO is equivalent to the BIO. However, direct implementation of the HO requires inversion of a huge covariance matrix for high-dimensional imaging data, which can be computationally challenging. To address this challenge, imaging data are often projected onto a low-dimensional space through a set of channels. The Hotelling observer (HO) can subsequently be applied to the resulting channelized data, forming the channelized Hotelling observer (CHO). However, channelized data may not be Gaussian distributed and the corresponding ideal discriminant function may not be linear. The Box-Cox transformation is a statistical method developed to transform non-Gaussian distributed data such that the transformed data more closely follow a Gaussian distribution. In this work, I introduce a nonlinear MO that integrates channel mechanisms and the Box-Cox transformation. The proposed observer, termed the Channelized MO with Box-Cox (CMO-BC), transforms the channelized data using the Box-Cox method and applies the HO to the nonlinearly transformed data. Numerical studies are conducted for a binary signal detection task that involves a stochastic lumpy background model. It is demonstrated that the signal detection performance of the proposed CMO-BC can significantly outperform that of the CHO and the HO. The findings suggest that the CMO-BC has the potential to serve as a computationally efficient nonlinear MO for the objective assessment of image quality.